化简:sin7°+cos15°sin8°cos7°−sin15°sin8°.
问题描述:
化简:
. sin7°+cos15°sin8° cos7°−sin15°sin8°
答
因为cos15°sin8°=
[sin(8°+15°)+sin(8°-15°)=1 2
(sin23°-sin7°)],1 2
sin15°sin8°=
(cos7°-cos23°),1 2
所以
=sin7°+cos15°sin8° cos7°−sin15°sin8°
sin23°+sin7° cos23°+cos7°
=
=tan15°=tan(45°-30°)2sin15°cos8° 2cos15°cos8°
=
=2-tan45°−tan30° 1+tan45°tan30°
.
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